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Truncations of random orthogonal matrices

Boris A. Khoruzhenko, Hans-Jürgen Sommers, and Karol Życzkowski
Phys. Rev. E 82, 040106(R) – Published 19 October 2010

Abstract

Statistical properties of nonsymmetric real random matrices of size M, obtained as truncations of random orthogonal N×N matrices, are investigated. We derive an exact formula for the density of eigenvalues which consists of two components: finite fraction of eigenvalues are real, while the remaining part of the spectrum is located inside the unit disk symmetrically with respect to the real axis. In the case of strong nonorthogonality, M/N=const, the behavior typical to real Ginibre ensemble is found. In the case M=NL with fixed L, a universal distribution of resonance widths is recovered.

  • Figure
  • Figure
  • Received 12 August 2010

DOI:https://doi.org/10.1103/PhysRevE.82.040106

©2010 American Physical Society

Authors & Affiliations

Boris A. Khoruzhenko1, Hans-Jürgen Sommers2, and Karol Życzkowski3,4

  • 1Queen Mary University of London, School of Mathematical Sciences, London E1 4NS, United Kingdom
  • 2Fakultät für Physik, Universität Duisburg–Essen, 47048 Duisburg, Germany
  • 3Smoluchowski Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
  • 4Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotników 32/44, 02-668 Warszawa, Poland

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Issue

Vol. 82, Iss. 4 — October 2010

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